How to use this proportion calculator
Choose a, b, c, or d as the missing term. The selected field becomes x. Enter valid decimals in the remaining three positions, keeping corresponding quantities in the same order and compatible units. The result updates immediately. A value that would create division by zero produces an error instead of a misleading answer.
How the calculation works
A proportion says that two ratios or fractions are equal: a/b = c/d. Cross-multiplication follows because multiplying both sides by b and d gives a × d = b × c. Once three terms are known, isolate the missing term by dividing the known cross-product by the remaining term.
Correct correspondence matters more than the arithmetic. If the first ratio is miles to hours, the second must also be miles to hours. Converting compatible units before entering values prevents a mathematically consistent equation from representing the wrong real-world comparison.
Formulas
Cross-product rule
Solve for d
Solve any position
Worked examples
Solve 2:3 = 10:x
Cross-multiply to get 2x = 30. Divide by 2, so x = 15 and 2/3 = 10/15.
Scale a recipe
If 2.5 cups serve 4 people, the proportion 2.5/4 = x/10 gives x = 6.25 cups for ten equal servings.
Common uses
Recipes and scaling
Increase or reduce quantities while preserving the same relative relationship. Match ingredient to serving positions consistently before solving the missing amount.
Maps, models, and rates
Solve scale drawings, map distances, unit prices, speeds, and other equivalent-rate questions. Convert units first when corresponding terms use different measurement systems.
Classroom algebra
Verify cross-multiplication and isolate any of the four terms in a proportion. The exact fraction makes non-whole-number answers visible instead of silently rounding them.
Accuracy and limitations
The calculator converts entered decimals to exact fractions, applies the cross-product identity, and returns both exact and readable decimal forms. Repeating decimals are marked when shortened for display.
A proportion is valid only when corresponding quantities are arranged in the same order and denominators are nonzero. Context-specific formulas may be nonlinear and should not be forced into a simple proportion.
Frequently asked questions
What is a proportion?
A proportion is an equation stating that two ratios are equal. The relationship is valid when their cross-products are equal.
Can I solve for any of the four terms?
Yes. Select the missing letter from the menu, then enter the other three values.
Can the answer be a fraction or decimal?
Yes. The calculator displays both a decimal form and an exact simplified fraction whenever the result is not a whole number.
Why must corresponding units match?
The two ratios must compare the same kinds of quantities in the same order. Convert compatible units first and label each position.
Can a proportion contain zero?
Some terms may be zero, but neither denominator may be zero and the algebra used to isolate the missing value must not divide by zero.
Is the proportion calculator free to use?
Yes. NumUtility is free, requires no account, and places no limit on ordinary calculations.
Are my entries stored?
No. The calculation runs in your browser. Values entered into the tool are not sent to NumUtility or saved by us.